1. The graph below represents the distance in meters that a skydiver has fallen t seconds after jumping out of a plane.
(a) Use the graph to estimate the velocity of the skydiver at t = 10 and t = 20. Explain how you obtained your estimates. (You might start by drawing a tangent line at t = 10, then estimating two points on that line, and computing rise over run.)
(b) Use the graph to estimate the velocity of the skydiver at t = 80. Explain how you obtained your estimate.
(c) Sketch a graph of the velocity of the skydiver. Make sure your sketch is consistent with (a) and (b).
(d) The function modeling the distance the skydiver has fallen can be written
s(t) = { at^2 if 0 <= t <= 30
mt + b if t >= 30
for some numbers a, m, and b. What are the numbers a, m, and b? Explain how you found them.
(e) Use the formula in part (d) to compute s'(10), s'(20), and s'(80) and relate it to your answers from (a) and (b).
(f) Describe what happened to the velocity at time t = 30. What do you think caused this?